Math Monday: Stained Glass Polar Zonohedron

by George Hart

Stained glass can be used to make many mathematical forms. One very beautiful shape is the polar zonohedron. Hans Schepker made this three-foot diameter example from hundreds of pieces of stained glass.Below, you can see Hans soldering it together while supporting the partially assembled lamp in a hammock. His construction approach is based on 5-by-5 modules which fit into a brass framework.A view along the axis is quite spectacular. You can see it consists of twenty spirals in each direction. Every spiral strip is geometrically identical, with a slightly different quadrilateral shape required at each position along the spiral. Many construction photos can be seen on Hans’s website, here. Be sure to observe how the modules divide it structurally with four-way rotational symmetry, but the color pattern has five-way symmetry, so the colors had to be planned differently on each module.